Conventionally, the prediction coding technique of this type is utilized for data compression that aims at efficiently utilizing a record medium and a transmission path when the two-dimensional signal, which is typified by an image signal, is stored in a record medium, or is transmitted via a network.
There exists the technique of predicting a value of a target pixel from neighboring pixels (upper/left/left upper side, etc.) already coded, and coding a residual (for example, see Patent document 1) as a general technique of the conventional prediction coding. FIG. 10 shows an example of the general prediction technique. A matrix prediction technique predicts a value of a target pixel X from a left-side pixel A and an upper-side pixel C, an average prediction technique predicts the value of the target pixel X from the left-side pixel A and a right upper-side pixel D, and a plane prediction technique predicts the value of the target pixel X from the left pixel A, a left upper-side pixel B, and the upper-side pixel C. Any of these techniques is characterized in that an equation for computing the predicted value is simple, and hence a high processing speed is attained to that extent. There exists JPEG-LS as a representative of the prediction coding adopting this technique.
There exists the technique of firstly coding low-resolution images sub-sampled from an original image at every interval of predetermined pixels, next predicting the value of the remaining not-yet-coded pixel from the already-coded pixels with an interpolation, and coding a residual thereof as another technique of the conventional prediction coding (for example, see Non-patent document 1, patent document 2, and Patent document 3). The point that a resolution progressive function can be realized is listed as an advantageous point of this technique. With this, only the low-resolution component of the image can be extracted, decoded, and displayed even though it is a gigantic image, thereby enabling a cognitive waiting time of a user to be reduced.
The technique of predicting the value of the not-yet-coded pixel from the already-coded pixels in the prediction coding having the resolution progressive function includes the technique of predicting it only by using the pixel of the previous resolution (for example, see Non-patent document 1, and Patent document 3), and the technique of predicting it by using the pixel of the previous resolution and the pixel of the present resolution together (for example, see 0004 paragraph of Patent document 2).
On the other hand, a Huffman code, a Golomb-Rice code, etc. are known as a variable length code suitable for coding the prediction residual. Particularly, the Golomb-Rice coding technique, which is for outputting the signal value as [unary]+[k-bit fixed-length code (k is an estimated value of the number of significant figures)], is known as a technique for simply coding the prediction residual because nearer to zero the value is, the shorter the code length becomes. Further, the Golomb-Rice code is characterized in that when the number of significant figures of the signal value that should be coded, and a k value coincide with each other, the code length becomes shortest, whereby an adaptive Golomb-Rice coding technique for predicting an optimum k value responding to values of residuals that have occurred so far, and the contexts has been devised. For example, the adaptive Golomb-Rice coding technique described in Patent document 4 is a technique of predicting an optimum k value from the distribution of prediction residuals d. Specifically, an absolute value of each of the prediction residuals d that have occurred so far is accumulated, and an average number of significant figures is estimated from its sum total a and the number of times n of the accumulation.    Non-Patent document 1: “Fast Progressive Lossless Image Compression”, Proceedings of the 1994 IST/SPIE, 1994/02    Patent document 1: Specification of U.S. Pat. No. 5,680,129    Patent document 2: JP-P2501598B    Patent document 3: JP-P2005-198014A    Patent document 4: Specification of U.S. Pat. No. 5,764,374